Two remarks on transcendental shift-like maps on $\mathbb{C}^N$
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866909004488245248 |
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| author | Kaur, Ramanpreet |
| author_facet | Kaur, Ramanpreet |
| contents | In \cite{Bedford}, the dynamics of a particular polynomial diffeomorphism of $\mathbb{C}^N$, called a polynomial shift-like map of type $ν$, has been studied as a higher dimensional analog of Hénon maps. In this note, we prove that the Julia set of their transcendental counterpart is non-empty. In addition, an example of a transcendental shift-like map with an escaping wandering domain has been provided which, in fact, showcases a contrast with the dynamics of a polynomial shift map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27832 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Two remarks on transcendental shift-like maps on $\mathbb{C}^N$ Kaur, Ramanpreet Dynamical Systems Complex Variables 30D05, 37F10 In \cite{Bedford}, the dynamics of a particular polynomial diffeomorphism of $\mathbb{C}^N$, called a polynomial shift-like map of type $ν$, has been studied as a higher dimensional analog of Hénon maps. In this note, we prove that the Julia set of their transcendental counterpart is non-empty. In addition, an example of a transcendental shift-like map with an escaping wandering domain has been provided which, in fact, showcases a contrast with the dynamics of a polynomial shift map. |
| title | Two remarks on transcendental shift-like maps on $\mathbb{C}^N$ |
| topic | Dynamical Systems Complex Variables 30D05, 37F10 |
| url | https://arxiv.org/abs/2604.27832 |